Find the value

Question:

If $5 \mathrm{~A}=\left[\begin{array}{ccc}5 & 10 & -15 \\ 2 & 3 & 4 \\ 1 & 0 & -5\end{array}\right]$, find $\mathrm{A}$.

Solution:

$5 A=\left[\begin{array}{ccc}5 & 10 & -15 \\ 2 & 3 & 4 \\ 1 & 0 & -5\end{array}\right]$

$A=\left[\begin{array}{ccc}\frac{5}{5} & \frac{10}{5} & \frac{-15}{5} \\ \frac{2}{5} & \frac{3}{5} & \frac{4}{5} \\ \frac{1}{5} & \frac{0}{5} & \frac{-5}{5}\end{array}\right]$

$A=\left[\begin{array}{ccc}1 & 2 & -3 \\ \frac{2}{5} & \frac{3}{5} & \frac{4}{5} \\ \frac{1}{5} & 0 & -1\end{array}\right]$

Conclusion: $A=\left[\begin{array}{ccc}1 & 2 & -3 \\ \frac{2}{5} & \frac{3}{5} & \frac{4}{5} \\ \frac{1}{5} & 0 & -1\end{array}\right]$

 

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